arXiv subjects

Le Van Hien

Publications and source records attributed to Le Van Hien.

9 recordsLinked to original sources

arXiv2026

Variational Analysis of Metric Projections onto Isotone Projection Cones via Coderivatives

In this paper, we study variational properties of the metric projection mapping onto isotone projection cones in finite-dimensional Euclidean spaces. We derive explicit formulas for both the Fréchet coderivative and the Mordukhovich coderivative of the projection operator. The analysis is based on a local description of the projection mapping via an associated generating system in a neighborhood of a reference point, which leads to computable coderivative characterizations. As an application, we compute the covering constant of the projection mapping, providing a quantitative description of its local regularity. Furthermore, we establish verifiable sufficient conditions for the Aubin property of the solution mapping associated with parametric nonlinear complementarity problems associated with isotone projection cones. The obtained results contribute to the variational analysis of metric projections in a general cone setting where orthogonality arguments are not available, and to the stability theory of complementarity systems in finite dimensions.

math.OC↗

arXiv2024

On the Coderivative of the Projection Operator onto the Positive Cone in Hilbert spaces

In this paper, we study the generalized differentiability of the metric projection operator onto the positive cone in Hilbert spaces. We first establish the formula for exactly computing the regular coderivative and the Mordukhovich coderivative of the metric projection operator onto the positive cone in Euclidean spaces. Then, these results are also established for the projection operator onto the positive cone in the real Hilbert space $l_2$.

math.FA↗

arXiv2024

Regular Coderivative and Graphical Derivative of the Metric Projection onto closed Balls in Hilbert spaces

In this paper, we first establish a formula for exactly computing the regular coderivative of the metric projection operator onto closed balls $r\mathbb{B}$ centered at the origin in Hilbert spaces. Then, this result is extended to metric projection operator onto any closed balls $\mathbb{B}(c,r)$, which has center $c$ in Hilbert space $H$ and with radius $r > 0$. Finally, we give the formula for calculating the graphical derivative of the metric projection operator onto closed balls with center at arbitrarily given point in Hilbert spaces.

math.FA↗

arXiv2024

Some Results on the Strict Fréchet Differentiability of the Metric Projection Operator in Hilbert Spaces

In this paper, we first present a simpler proof of a result on the strict Fréchet differentiability of the metric projection operator onto closed balls centered at the origin in Hilbert spaces, which given by Li in \cite{Li24}. Then, based on this result, we prove the strict Fréchet differentiability of the metric projection operator onto closed balls with center at arbitrarily given point in Hilbert spaces. Finally, we study the strict Fréchet differentiability of the metric projection operator onto the second-order cones in Euclidean spaces.

math.FA↗

arXiv2019

Second order optimality conditions for strong local minimizers via subgradient graphical derivative

This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We prove that the positive definiteness of the subgradient graphical derivative of an extended-real-valued lower semicontinuous proper function at a proximal stationary point is sufficient for the quadratic growth condition. It is also a necessary condition for the latter property when the function is either subdifferentially continuous, prox-regular, twice epi-differentiable or variationally convex. By applying our results to the $\mathcal{C}^2$-cone reducible constrained programs, we establish no-gap second order optimality conditions for (strong) local minimizers under the metric subregularity constraint qualification. These results extend the classical second order optimality conditions by surpassing the well-known Robinson's constraint qualification. Our approach also highlights the interconnection between the strong metric subregularity of subdifferential and quadratic growth condition in optimization problems.

math.OC↗

arXiv2017

Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming

This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of unconstrained optimization problems in terms of a uniform positive definiteness of the subgradient graphical derivative of the objective function around the point in question. By applying this result to nonlinear programming under the metric subregularity constraint qualification, we derive a second-order characterization and several new sufficient conditions for tilt stability. In particular, we show that each stationary point of a nonlinear programming problem satisfying the metric subregularity constraint qualification is a tilt-stable local minimizer if the classical strong second-order sufficient condition holds.

math.OC↗

arXiv2015

New summation inequalities and their applications to discrete-time delay systems

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.

math.OC↗

arXiv2015

On the existence and exponential attractivity of a unique positive almost periodic solution to an impulsive hematopoiesis model with delays

In this paper, a generalized model of hematopoiesis with delays and impulses is considered. By employing the contraction mapping principle and a novel type of impulsive delay inequality, we prove the existence of a unique positive almost periodic solution of the model. It is also proved that, under the proposed conditions in this paper, the unique positive almost periodic solution is globally exponentially attractive. A numerical example is given to illustrate the effectiveness of the obtained results.

math.CA↗

arXiv2004

Stability of Solutions of Fuzzy Differential Equations

In this paper, We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and comparison principle for Lyapunov - like functions, we give some sufficient criterias for the stability and asymptotic stability of solutions of fuzzy differential equations.

math.DS↗